The sound source actually lies on a hyperbola described by deltaT = (r0 - r1)/c where r0 is the range from the emitter to microphone 0 and r1 is emitter to microphone 1.
The cosine formula describes a cone which the hyperbola asymptotically approaches with increasing range. Thus the cosine formula is strictly correct only at infinite distance, but it's an increasingly reasonable approximation beyond about 5x the microphone baseline distance.
To solve the hyperbola formulation, you need to know the range to the emitter which requires a third microphone at a minimum.